GATE EC-3

1. Q.1 The strategies that the company to sell its products house-to-house marketing.

2. He was not only accused of theft ……. of conspiracy.

3. Select the word that fits the analogy: Explicit: Implicit:: Express: …………..

4. The Canadian constitution requires that equal importance be given to English and French. Last year. Air Canada lost a lawsuit, and had to pay a six-figure fine to a Frenchspeaking couple after they filed complaints about formal in-flight announcements in English lasting 15 seconds, as opposed to informal 5 second messages in French, The French-speaking couple were upset at

5. A super additive function n f (.) satisfies the following property f x x f x f x ( 1 2 1 2 +  + ) ( ) ( ) Which of the following functions is a super additive function for x > 1?

6. The global financial crisis in 2008 is considered to be the most serious world-wide financial crisis, which started with the sub-prime lending crisis in USA in 2007. The subprime lending crisis led to the banking crisis in 2008 with the collapse of Lehman Brothers in 2008. The sub-prime lending refers to the provision of loans to those borrowers who may have difficulties in repaying loans, and it arises because of excess liquidity following the East Asian crisis. Which one of the following sequences shows the correct precedence as per the given passage?

7. It is quarter past three in your watch. The angle between the hour hand and the minute hand

8. A single crystal intrinsic semiconductor is at temp of 300 K with effective density of states for holes twice that of electrons. VT = 26 mV. The intrinsic Fermi level is shifted from mid bond gap energy level by

9. Consider the recombination process via bulk traps in a forward biased pn homojunction diode. The maximum recombination rate is Umax. If the electron and the hole capture cross-sections are equal, which one of the following is FALSE?

10. A digital communication system transmits a block of N bits. The probability of error in decoding a bit is a α. The error event of each bit is independent of error events of other bits. The received block is declared erroneous if at least one of the bits is decoded wrongly. The probability that the received block is erroneous is

11. If v1, v2,...,v6 are six vectors in R4 , which one of the following statements is FALSE?

12. The general solution of 2 2 d y dy 6 9y 0 dx dx − + = is

13. The impedances Z = jX, for all X in the range (—∞,∞), map to the Smith chart as

14. The partial derivative of the function F(x, y, z) = e1-x cos y + xze-1/(1+y2) With respect to x at the point (1, 0, e) is

15, The characteristic equation of a system is s3 + 3s2 + (K + 2)s + 3K = 0 In the root locus plot for the given system, as K varies from 0 to ∞, the break-away or break-in point(s) lie within

16. P, Q and R are the decimal integers corresponding to the 4-bit binary number 1100 considered in signed magnitude, 1’s complement, and 2’s complement representations, respectively. The 6-bit 2’s complement representation of (P + Q + R) is

17. A rule states that in order to drink beer, one must be over 18 years old. In a bar, there are 4 people. P is 16 years old, Q is 25 years old, R is drinking milkshake and S is drinking a beer. What must be checked to ensure that the rule is being followed?

18. The ninth and the tenth of this month are Monday and Tuesday ________

19. 500 students are taking one or more courses out of chemistry, physics and Mathematics. Registration records indicate course enrolment as follows: chemistry (329), physics (186), Mathematics (295), chemistry and physics (83), chemistry and Mathematics (217), and physics and Mathematics (63), How many students are taking all 3 subjects

20. It _________ to read this year’s textbook _________ the last year’s

21. Fatima starts form point P, goes North for 3km, and then East for 4 km to reach point Q. She then turns to face point P and goes 15km in that direction. She then goes North for 6km. How far is she from point P, and in which direction should she go to reach point P?

22. “If you are looking for a history of India, or for an account of the rise and fall of the British Raj, or for the reason of the cleaving of the subcontinent into two mutually antagonistic parts and the effects this mutilation will have in the respective sections, and ultimately on Asia, you will not find it in these pages; for though I have spent a lifetime in the country. I lived too near the seat of events, and was too intimately associated with the actors, to get the perspective needed for the impartial recording of these matters”. Which of the following statements best reflects the author’s opinion?

23. The number of 3-digit numbers such that the digit 1 is never to the immediate right of 2 is

24. 1200 men and 500 women can build a bridge in 2 weeks. 900 men and 250 women will take 3 weeks to build the same bridge. How many men will be needed to build the bridge in one week?

25. Which of the following statement is incorrect?

26. In a DRAM,

27. An n-channel enhancement mode MOSFET is biased at VGS>VTH and VDS>(VGS−VTH), where VGS is the gate to source voltage, VDS is the drain to source voltage and VTH is the threshold voltage. Considering channel length modulation effect to be significant, the MOSFET behaves as a ______

28.Which of the following options is the closest in meaning to the word underlined in the sentence below? In a democracy, everybody has the freedom to disagree with the government.

29. After the discussion, Tom said to me, 'Please revert!’ He expects me to _________.

30. While receiving the award, the scientist said, "I feel vindicated". Which of the following is closest in meaning to the word ‘vindicated

31. In a sequence of 12 consecutive odd numbers, the sum of the first 5 numbers is 425. What is the sum of the last 5 numbers in the sequence?

32. Find the next term in the sequence: 13M, 17Q, 19S, ___

33. If ‘KCLFTSB’ stands for ‘best of luck’ and ‘SHSWDG’ stands for ‘good wishes’, which of the following indicates ‘ace the exam’?

34. Industrial consumption of power doubled from 2000- 2001 to 2010-2011. Find the annual rate of increase in percent assuming it to be uniform over the years.

35. A five-digit number is formed using the digits 1,3,5,7 and 9 without repeating any of them. What is the sum of all such possible five digit numbers?

36. For a given sample-and-hold circuit, if the value of the hold capacitor is increased, then

37. In a Bode magnitude plot, which one of the following slopes would be exhibited at high frequencies by a 4th order all-pole system?

38. If calls arrive at a telephone exchange such that the time of arrival of any call is independent of the time of arrival of earlier or future calls, the probability distribution function of the total number of calls in a fixed time interval will be

39. In a double side-band (DSB) full carrier AM transmission system, if the modulation index is doubled, then the ratio of total sideband power to the carrier power increases by a factor of_________________.

40. Parcels from sender S to receiver R pass sequentially through two post-offices. Each post-office has a probability 1 5 of losing an incoming parcel, independently of all other parcels. Given that a parcel is lost, the probability that it was lost by the second post-office is_________.

41. For a right angled triangle, if the sum of the lengths of the hypotenuse and a side is kept constant, in order to have maximum area of the triangle, the angle between the hypotenuse and the side is

42. A BJT in a common-base configuration is used to amplify a signal received by a 50  antenna. Assume kT/q = 25 mV. The value of the collector bias current (in mA) required to match the input impedance of the amplifier to the impedance of the antenna is________.

43. An M-level PSK modulation scheme is used to transmit independent binary digits over a band-pass channel with bandwidth 100 kHz. The bit rate is 200 kbps and the system characteristic is a raised-cosine spectrum with 100% excess bandwidth. The minimum value of M is ________.

44. “India is a country of rich heritage and cultural diversity.” Which one of the following facts best supports the claim made in the above sentence?

45. The value of one U.S. dollar is 65 Indian Rupees today, compared to 60 last year. The Indian Rupee has ____________.

46. 'Advice' is ________________.

47. The next term in the series 81, 54, 36, 24 … is ________

48. Find the next term in the sequence: 7G, 11K, 13M, ___

49. A man can row at 8 km per hour in still water. If it takes him thrice as long to row upstream, as to row downstream, then find the stream velocity in km per hour.

50. A batch of one hundred bulbs is inspected by testing four randomly chosen bulbs. The batch is rejected if even one of the bulbs is defective. A batch typically has five defective bulbs. The probability that the current batch is accepted is _________

51. In MOSFET fabrication, the channel length is defined during the process of

52. A thin P-type silicon sample is uniformly illuminated with light which generates excess carriers. The recombination rate is directly proportional to

53. The desirable characteristics of a transconductance amplifier are

54. An analog voltage in the range 0 to 8 V is divided in 16 equal intervals for conversion to 4-bit digital output. The maximum quantization error (in V) is

55. Which one of the following statements is NOT true for a square matrix?

56. A fair coin is tossed repeatedly till both head and tail appear at least once. The average number of tosses required is __________________.

57. Choose the most appropriate word from the options given below to complete the following sentence. Communication and interpersonal skills are_____ important in their own ways.

58. Which of the options given below best completes the following sentence? She will feel much better if she ________________.

59. Choose the most appropriate pair of words from the options given below to complete the following sentence. She could not _____ the thought of _________ the election to her bitter rival.

60. Fill in the missing number in the series. 2 3 6 15 ___ 157.5 630

61. Find the odd one in the following group Q, W, Z, B B, H, K, M W, C, G, J M, S, V, X

62. Lights of four colors (red, blue, green, yellow) are hung on a ladder. On every step of the ladder there are two lights. If one of the lights is red, the other light on that step will always be blue. If one of the lights on a step is green, the other light on that step will always be yellow. Which of the following statements is not necessarily correct?

63. The sum of eight consecutive odd numbers is 656. The average of four consecutive even numbers is 87. What is the sum of the smallest odd number and second largest even number?

64. It takes 30 minutes to empty a half-full tank by draining it at a constant rate. It is decided to simultaneously pump water into the half-full tank while draining it. What is the rate at which water has to be pumped in so that it gets fully filled in 10 minutes?

65. The determinant of matrix A is 5 and the determinant of matrix B is 40. The determinant of matrix AB is ________.